Question

在抛物线y=-x²上取三点A,B,C,设A,B的横坐标分别为 a,a+1(a>0),直线BC与x轴平行

Answer 1

(1)

A(a,-a²),B((a+1),-(a+1)²)

该抛物线的对称轴为y轴,C与B关于y轴对称,C(-(a+1),-(a+1)²)

CB= (a+1)+(a+1) = 2(a+1)

CB上的高h为A,B纵坐标之差,h = -a² +(a+1)² = 2a+1

s = (1/2)*2(a+1)*(2a+1) = (a+1)(2a+1)

(2) s = 15

(a+1)(2a+1) = 15

(2a+7)(a-2) = 0

a = 2 (-7/2 < 0 舍去)

(3)△ABC和△ACD在CD(或CB)上的高均为2a+1,要使△ACD的面积为8(s的8/15),只需CD:CB = 8:15即可.

CB= 2(a+1) = 6

CD:CB = x :6 = 8:15

x = 16/5

C(-3,-9)

D纵坐标:-3 + 16/5 = 1/5

D(1/5,-9)